The biggest movement in this vote is by the Slovakian Foreign Minister, Miroslav Lajcak, who has moved into second spot from the depths of seventh in the first ballot to 10th in the second ballot.
He is playing a prominent role in the European Union at present with Slovakia holding the presidency of the EU for six-months.
The highest ranking women candidate in this ballot are Irina Bokova of Bulgaria, favoured by Russia, and Susana Malcorra of Argentina, favoured by the United States.
They both have seven "encourage" votes but Bokova has fewer "discourage" votes than Malcorra.
Helen Clark is in Cameroon in Africa in her capacity as head of the United Nations Development Fund.
She responded to the latest poll results by tweeting "La lucha continua" - Spanish for 'the struggle continues.'
In the tweet, Clark wrote: "many thanks to UN Security Council members for continued support for #Helen4SG. La lucha continua."
The phrase is most closely linked to Argentinian Marxist revolutionary Che Guevera, who reportedly used it when leaving Cuba for Bolivia: "la lucha continua no terminara facilmente' [the struggle continues, it will not end easily.]
On a regional rotational basis, it is considered Eastern Europe's turn - a view strongly held by Russia - although countries supporting that view have not got behind a single candidate.
Foreign Minister Murray McCully told the Herald he had just spoken to Clark in Cameroon and he saw no need for her to withdraw.
"It is a perfectly respectable result from Helen Clark's point of view.
"It is still the case that the Eastern European sort-out is going to occur before there is room for others."
Guterres had done pretty well although there was no clear picture emerging.
"Simply what we had always expected which is that some time in October people are going to sit down and do some serious horse-trading.
"And Helen Clark is not out of that picture at all."
It is possible a fourth straw poll could be held in September during a month of New Zealand's presidency of the Security Council.
If that did happen, Russia would conduct the ballot, given New Zealand has a candidate.
At present, it is not known which candidates are attracting "discourage" votes from the five Security Council members with a veto.
During past selections for Secretary General, at later ballots the P5 votes are a different colour to the elected members ballots in order to tell which candidates could attract a veto.
Today's ranking based on highest number of "encourage" votes (followed by first-round then second-round rankings).
Third round:
1. Antonio Guterres, Portugal (1, 1)
2. Miroslav Lajcak, Slovakia (7, 10)
3= Irina Bokova, Bulgaria (3, 5)
3= Vuk Jeremic, Serbia (4, 2)
5. Susana Malcorra, Argentina (8, 3)
6. Srgjan Kerim, Macedonia (5, 6)
7. Helen Clark, New Zealand (6, 7)
8. Danilo Turk, Slovenia (2, 4)
9= Christiana Figueres, Costa Rica (9, 8)
9= Natalia Gherman, Moldova (10, 9)
The following are the actual ratings each candidate got in today's ballot from the three choices, "encourage," "discourage," or "no opinion."
Antonio Guterres, Portugal: 11 - 3 - 1
Miroslav Lajcak, Slovakia: 9 - 5 - 1
Irina Bokova, Bulgaria: 7 - 5 - 3
Vuk Jeremic, Serbia: 7 - 5 - 3
Susana Malcorra, Argentina: 7 - 7 - 1
Srgjan Kerim, Macedonia: 6 - 7 - 2
Helen Clark, New Zealand: 6 - 8 - 1
Danilo Turk, Slovenia: 5 - 6 - 4
Christiana Figueres, Costa Rica: 2 - 12 - 1
Natalia Gherman, Moldova: 2 - 12 - 1
Security Council members
• Angola
• Egypt
• Japan
• Malaysia
• New Zealand
• Senegal
• Spain
• Ukraine
• Uruguay
• Venezuela
With veto
• Britain
• China
• France
• Russia
• United States
